Samy Abo Seada, Joseph V Hajnal and Shaihan J Malik A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients Samy Abo Seada, Joseph V Hajnal and Shaihan J Malik

Motivation Aim Problem: Multiband RF pulses for SMS have long pulse durations [1,2] Solution: Use Time-Optimal VERSE to reduce pulse duration [3] Result: Not suitable for gradient system due to gradient imperfection Our solution: Iterative VERSE optimization with gradient correction Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion 5059 - A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients [1] Larkman et al. 2001 [2] Wong E. 2012 [3] Lee et al. 2009

Theory (1) - VERSE algorithm Aim For flip angle 𝜃 RF flips Magnetization down by an angle 𝜃 and gradient ensures spatial selection Ultimately, net rotation 𝜃 determined by angular precession [4] To achieve same signal, preserve net rotation 𝜃. Net rotation preserved if field strengths are halved and played out twice as long Theory VERSE TO-VERSE GIRF-effect 𝜃=𝜔 dt Iterative RF-correction Methods Results Simulations Experiment Same net rotation 𝜃 Conclusion 5059 - A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients [4] Conolly 1988

Theory (2) Time Optimal VERSE Aim Use VERSE to Minimise pulse duration, given System specification [5] Max gradient amplitude, max slew rate, max B1 Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion Define arc-length parameter 𝑠 𝑡 =𝛾 0 𝑡 𝐺 𝜏 𝑑𝜏 Excitation profiles preserved if 𝑊 𝑠 = 𝐵 1 𝑠 𝐺(𝑠) = 𝐵 1 𝑣 (𝑠) 𝐺 𝑣 (𝑠) 5059 - A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients [5] Lee et al 2009

Theory (3) GIRF-effect Aim Previous work: Use VERSE to Minimise pulse duration, given hardware specs Does: Maximum peak RF (13𝜇𝑇), Maximum peak Gradient (40 𝑚𝑇 𝑚 ), Maximum slew-rate (200 𝑚𝑇 𝑚 𝑚𝑠 ) Does not take into account: Eddy currents, RF/G time-mismatch etc.. A measured Gradient Impulse Response function (GIRF) does! Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations 𝐺 𝑜𝑢𝑡 (𝑡)= 𝐺 𝑖𝑛 (𝑡)∗𝐺𝐼𝑅𝐹(𝑡) Experiment Conclusion 5059 - A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients [6] Vannesjo 2013

Theory (3) GIRF-effect Simulated Profiles Gradient after TO-VERSE RF after TO-VERSE Aim Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Simulated Profiles Results Simulations Experiment Conclusion 5059 - A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

Theory (4) Iterative correction Aim Holds for But Magnetization experiences Correct by substituting 𝑠 𝑎𝑐𝑡 into (1) and find 𝐵 1,𝑎𝑐𝑡𝑢𝑎𝑙 𝑣 𝑠 𝑎𝑐𝑡 =𝑊 𝑠 𝑎𝑐𝑡 𝐺 𝑎𝑐𝑡𝑢𝑎𝑙 𝑣 ( 𝑠 𝑎𝑐𝑡 ) Excitation profiles preserved if 𝑊 𝑠 = 𝐵 1 𝑠 𝐺(𝑠) = 𝐵 1 𝑣 (𝑠) 𝐺 𝑣 (𝑠) (1) Theory VERSE Corrected RF pulse overshoots initial 𝐵 1 constraint TO-VERSE GIRF-effect 𝑠 𝑡 =𝛾 0 𝑡 𝐺 𝑑𝑒𝑚𝑎𝑛𝑑 𝑣 𝜏 𝑑𝜏 Iterative RF-correction Methods Simulated Profiles Results Simulations | 𝑀 𝑥𝑦 | 𝑠 𝑎𝑐𝑡 𝑡 =𝛾 0 𝑡 𝐺 𝑎𝑐𝑡𝑢𝑎𝑙 𝑣 𝜏 𝑑𝜏 Experiment Conclusion Space [cm] 5059 - A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

Theory (4) Iterative correction Aim Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion 5059 - A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

Methods Aim Simulations: Phase-optimized [Wong 2012] 180 𝑜 refocusing pulses Maximum gradient 40 𝑚𝑇 𝑚 . Peak 𝐵 1 : 13𝜇𝑇 Maximum slew-rate: 200 𝑚𝑇 𝑚 𝑚𝑠 GIRF: Measured for our Philips Achieva 3T Experiments: Philips Achieva 3T. Gradient echo sequence Spherical water phantom ( 𝑇 1 =270ms) Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion 5059 - A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

Results (1): Simulations Aim Effective duration defined as 𝑇 𝑒𝑓𝑓 = 𝛾 𝐵 1,𝑚𝑎𝑥 𝑑𝑡 𝜃 where 𝛾:gyromagnetic ratio. dt: dwell-time. 𝜃: Flip angle Errorsbars show range of duration across different slice-separations Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion VERSE:80% reduction VERSE + GIRF: 70 reduction VERSE:46% reduction VERSE + GIRF: 31% reduction 5059 - A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

Results (2) – In-vitro experiment Aim Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion 5059 - A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients

Conclusion Aim Effective method to make Time-optimal VERSE-Multiband pulses feasible Applicable for any 1D pulse which suffers from gradient BW problems Three-stage design is sub-optimal High compression factor for Higher Time-bandwidth pulses Further work: Incorporate GIRF directly into VERSE for optimal design Is a measured GIRF necessary? Theory VERSE TO-VERSE GIRF-effect Iterative RF-correction Methods Results Simulations Experiment Conclusion 5059 - A simple optimization approach to making time efficient VERSE-multiband pulses feasible on non-ideal gradients